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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.geometry.partitioning;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.lang.reflect.Array;<a name="line.19"></a>
<FONT color="green">020</FONT>    import java.util.ArrayList;<a name="line.20"></a>
<FONT color="green">021</FONT>    import java.util.Collection;<a name="line.21"></a>
<FONT color="green">022</FONT>    import java.util.Comparator;<a name="line.22"></a>
<FONT color="green">023</FONT>    import java.util.Iterator;<a name="line.23"></a>
<FONT color="green">024</FONT>    import java.util.TreeSet;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.MathInternalError;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.geometry.Space;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.geometry.Vector;<a name="line.28"></a>
<FONT color="green">029</FONT>    <a name="line.29"></a>
<FONT color="green">030</FONT>    /** Abstract class for all regions, independently of geometry type or dimension.<a name="line.30"></a>
<FONT color="green">031</FONT>    <a name="line.31"></a>
<FONT color="green">032</FONT>     * @param &lt;S&gt; Type of the space.<a name="line.32"></a>
<FONT color="green">033</FONT>     * @param &lt;T&gt; Type of the sub-space.<a name="line.33"></a>
<FONT color="green">034</FONT>    <a name="line.34"></a>
<FONT color="green">035</FONT>     * @version $Id: AbstractRegion.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.35"></a>
<FONT color="green">036</FONT>     * @since 3.0<a name="line.36"></a>
<FONT color="green">037</FONT>     */<a name="line.37"></a>
<FONT color="green">038</FONT>    public abstract class AbstractRegion&lt;S extends Space, T extends Space&gt; implements Region&lt;S&gt; {<a name="line.38"></a>
<FONT color="green">039</FONT>    <a name="line.39"></a>
<FONT color="green">040</FONT>        /** Inside/Outside BSP tree. */<a name="line.40"></a>
<FONT color="green">041</FONT>        private BSPTree&lt;S&gt; tree;<a name="line.41"></a>
<FONT color="green">042</FONT>    <a name="line.42"></a>
<FONT color="green">043</FONT>        /** Size of the instance. */<a name="line.43"></a>
<FONT color="green">044</FONT>        private double size;<a name="line.44"></a>
<FONT color="green">045</FONT>    <a name="line.45"></a>
<FONT color="green">046</FONT>        /** Barycenter. */<a name="line.46"></a>
<FONT color="green">047</FONT>        private Vector&lt;S&gt; barycenter;<a name="line.47"></a>
<FONT color="green">048</FONT>    <a name="line.48"></a>
<FONT color="green">049</FONT>        /** Build a region representing the whole space.<a name="line.49"></a>
<FONT color="green">050</FONT>         */<a name="line.50"></a>
<FONT color="green">051</FONT>        protected AbstractRegion() {<a name="line.51"></a>
<FONT color="green">052</FONT>            tree = new BSPTree&lt;S&gt;(Boolean.TRUE);<a name="line.52"></a>
<FONT color="green">053</FONT>        }<a name="line.53"></a>
<FONT color="green">054</FONT>    <a name="line.54"></a>
<FONT color="green">055</FONT>        /** Build a region from an inside/outside BSP tree.<a name="line.55"></a>
<FONT color="green">056</FONT>         * &lt;p&gt;The leaf nodes of the BSP tree &lt;em&gt;must&lt;/em&gt; have a<a name="line.56"></a>
<FONT color="green">057</FONT>         * {@code Boolean} attribute representing the inside status of<a name="line.57"></a>
<FONT color="green">058</FONT>         * the corresponding cell (true for inside cells, false for outside<a name="line.58"></a>
<FONT color="green">059</FONT>         * cells). In order to avoid building too many small objects, it is<a name="line.59"></a>
<FONT color="green">060</FONT>         * recommended to use the predefined constants<a name="line.60"></a>
<FONT color="green">061</FONT>         * {@code Boolean.TRUE} and {@code Boolean.FALSE}. The<a name="line.61"></a>
<FONT color="green">062</FONT>         * tree also &lt;em&gt;must&lt;/em&gt; have either null internal nodes or<a name="line.62"></a>
<FONT color="green">063</FONT>         * internal nodes representing the boundary as specified in the<a name="line.63"></a>
<FONT color="green">064</FONT>         * {@link #getTree getTree} method).&lt;/p&gt;<a name="line.64"></a>
<FONT color="green">065</FONT>         * @param tree inside/outside BSP tree representing the region<a name="line.65"></a>
<FONT color="green">066</FONT>         */<a name="line.66"></a>
<FONT color="green">067</FONT>        protected AbstractRegion(final BSPTree&lt;S&gt; tree) {<a name="line.67"></a>
<FONT color="green">068</FONT>            this.tree = tree;<a name="line.68"></a>
<FONT color="green">069</FONT>        }<a name="line.69"></a>
<FONT color="green">070</FONT>    <a name="line.70"></a>
<FONT color="green">071</FONT>        /** Build a Region from a Boundary REPresentation (B-rep).<a name="line.71"></a>
<FONT color="green">072</FONT>         * &lt;p&gt;The boundary is provided as a collection of {@link<a name="line.72"></a>
<FONT color="green">073</FONT>         * SubHyperplane sub-hyperplanes}. Each sub-hyperplane has the<a name="line.73"></a>
<FONT color="green">074</FONT>         * interior part of the region on its minus side and the exterior on<a name="line.74"></a>
<FONT color="green">075</FONT>         * its plus side.&lt;/p&gt;<a name="line.75"></a>
<FONT color="green">076</FONT>         * &lt;p&gt;The boundary elements can be in any order, and can form<a name="line.76"></a>
<FONT color="green">077</FONT>         * several non-connected sets (like for example polygons with holes<a name="line.77"></a>
<FONT color="green">078</FONT>         * or a set of disjoints polyhedrons considered as a whole). In<a name="line.78"></a>
<FONT color="green">079</FONT>         * fact, the elements do not even need to be connected together<a name="line.79"></a>
<FONT color="green">080</FONT>         * (their topological connections are not used here). However, if the<a name="line.80"></a>
<FONT color="green">081</FONT>         * boundary does not really separate an inside open from an outside<a name="line.81"></a>
<FONT color="green">082</FONT>         * open (open having here its topological meaning), then subsequent<a name="line.82"></a>
<FONT color="green">083</FONT>         * calls to the {@link #checkPoint(Vector) checkPoint} method will not be<a name="line.83"></a>
<FONT color="green">084</FONT>         * meaningful anymore.&lt;/p&gt;<a name="line.84"></a>
<FONT color="green">085</FONT>         * &lt;p&gt;If the boundary is empty, the region will represent the whole<a name="line.85"></a>
<FONT color="green">086</FONT>         * space.&lt;/p&gt;<a name="line.86"></a>
<FONT color="green">087</FONT>         * @param boundary collection of boundary elements, as a<a name="line.87"></a>
<FONT color="green">088</FONT>         * collection of {@link SubHyperplane SubHyperplane} objects<a name="line.88"></a>
<FONT color="green">089</FONT>         */<a name="line.89"></a>
<FONT color="green">090</FONT>        protected AbstractRegion(final Collection&lt;SubHyperplane&lt;S&gt;&gt; boundary) {<a name="line.90"></a>
<FONT color="green">091</FONT>    <a name="line.91"></a>
<FONT color="green">092</FONT>            if (boundary.size() == 0) {<a name="line.92"></a>
<FONT color="green">093</FONT>    <a name="line.93"></a>
<FONT color="green">094</FONT>                // the tree represents the whole space<a name="line.94"></a>
<FONT color="green">095</FONT>                tree = new BSPTree&lt;S&gt;(Boolean.TRUE);<a name="line.95"></a>
<FONT color="green">096</FONT>    <a name="line.96"></a>
<FONT color="green">097</FONT>            } else {<a name="line.97"></a>
<FONT color="green">098</FONT>    <a name="line.98"></a>
<FONT color="green">099</FONT>                // sort the boundary elements in decreasing size order<a name="line.99"></a>
<FONT color="green">100</FONT>                // (we don't want equal size elements to be removed, so<a name="line.100"></a>
<FONT color="green">101</FONT>                // we use a trick to fool the TreeSet)<a name="line.101"></a>
<FONT color="green">102</FONT>                final TreeSet&lt;SubHyperplane&lt;S&gt;&gt; ordered = new TreeSet&lt;SubHyperplane&lt;S&gt;&gt;(new Comparator&lt;SubHyperplane&lt;S&gt;&gt;() {<a name="line.102"></a>
<FONT color="green">103</FONT>                    public int compare(final SubHyperplane&lt;S&gt; o1, final SubHyperplane&lt;S&gt; o2) {<a name="line.103"></a>
<FONT color="green">104</FONT>                        final double size1 = o1.getSize();<a name="line.104"></a>
<FONT color="green">105</FONT>                        final double size2 = o2.getSize();<a name="line.105"></a>
<FONT color="green">106</FONT>                        return (size2 &lt; size1) ? -1 : ((o1 == o2) ? 0 : +1);<a name="line.106"></a>
<FONT color="green">107</FONT>                    }<a name="line.107"></a>
<FONT color="green">108</FONT>                });<a name="line.108"></a>
<FONT color="green">109</FONT>                ordered.addAll(boundary);<a name="line.109"></a>
<FONT color="green">110</FONT>    <a name="line.110"></a>
<FONT color="green">111</FONT>                // build the tree top-down<a name="line.111"></a>
<FONT color="green">112</FONT>                tree = new BSPTree&lt;S&gt;();<a name="line.112"></a>
<FONT color="green">113</FONT>                insertCuts(tree, ordered);<a name="line.113"></a>
<FONT color="green">114</FONT>    <a name="line.114"></a>
<FONT color="green">115</FONT>                // set up the inside/outside flags<a name="line.115"></a>
<FONT color="green">116</FONT>                tree.visit(new BSPTreeVisitor&lt;S&gt;() {<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>                    /** {@inheritDoc} */<a name="line.118"></a>
<FONT color="green">119</FONT>                    public Order visitOrder(final BSPTree&lt;S&gt; node) {<a name="line.119"></a>
<FONT color="green">120</FONT>                        return Order.PLUS_SUB_MINUS;<a name="line.120"></a>
<FONT color="green">121</FONT>                    }<a name="line.121"></a>
<FONT color="green">122</FONT>    <a name="line.122"></a>
<FONT color="green">123</FONT>                    /** {@inheritDoc} */<a name="line.123"></a>
<FONT color="green">124</FONT>                    public void visitInternalNode(final BSPTree&lt;S&gt; node) {<a name="line.124"></a>
<FONT color="green">125</FONT>                    }<a name="line.125"></a>
<FONT color="green">126</FONT>    <a name="line.126"></a>
<FONT color="green">127</FONT>                    /** {@inheritDoc} */<a name="line.127"></a>
<FONT color="green">128</FONT>                    public void visitLeafNode(final BSPTree&lt;S&gt; node) {<a name="line.128"></a>
<FONT color="green">129</FONT>                        node.setAttribute((node == node.getParent().getPlus()) ?<a name="line.129"></a>
<FONT color="green">130</FONT>                                                                                Boolean.FALSE : Boolean.TRUE);<a name="line.130"></a>
<FONT color="green">131</FONT>                    }<a name="line.131"></a>
<FONT color="green">132</FONT>                });<a name="line.132"></a>
<FONT color="green">133</FONT>    <a name="line.133"></a>
<FONT color="green">134</FONT>            }<a name="line.134"></a>
<FONT color="green">135</FONT>    <a name="line.135"></a>
<FONT color="green">136</FONT>        }<a name="line.136"></a>
<FONT color="green">137</FONT>    <a name="line.137"></a>
<FONT color="green">138</FONT>        /** Build a convex region from an array of bounding hyperplanes.<a name="line.138"></a>
<FONT color="green">139</FONT>         * @param hyperplanes array of bounding hyperplanes (if null, an<a name="line.139"></a>
<FONT color="green">140</FONT>         * empty region will be built)<a name="line.140"></a>
<FONT color="green">141</FONT>         */<a name="line.141"></a>
<FONT color="green">142</FONT>        public AbstractRegion(final Hyperplane&lt;S&gt;[] hyperplanes) {<a name="line.142"></a>
<FONT color="green">143</FONT>            if ((hyperplanes == null) || (hyperplanes.length == 0)) {<a name="line.143"></a>
<FONT color="green">144</FONT>                tree = new BSPTree&lt;S&gt;(Boolean.FALSE);<a name="line.144"></a>
<FONT color="green">145</FONT>            } else {<a name="line.145"></a>
<FONT color="green">146</FONT>    <a name="line.146"></a>
<FONT color="green">147</FONT>                // use the first hyperplane to build the right class<a name="line.147"></a>
<FONT color="green">148</FONT>                tree = hyperplanes[0].wholeSpace().getTree(false);<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>                // chop off parts of the space<a name="line.150"></a>
<FONT color="green">151</FONT>                BSPTree&lt;S&gt; node = tree;<a name="line.151"></a>
<FONT color="green">152</FONT>                node.setAttribute(Boolean.TRUE);<a name="line.152"></a>
<FONT color="green">153</FONT>                for (final Hyperplane&lt;S&gt; hyperplane : hyperplanes) {<a name="line.153"></a>
<FONT color="green">154</FONT>                    if (node.insertCut(hyperplane)) {<a name="line.154"></a>
<FONT color="green">155</FONT>                        node.setAttribute(null);<a name="line.155"></a>
<FONT color="green">156</FONT>                        node.getPlus().setAttribute(Boolean.FALSE);<a name="line.156"></a>
<FONT color="green">157</FONT>                        node = node.getMinus();<a name="line.157"></a>
<FONT color="green">158</FONT>                        node.setAttribute(Boolean.TRUE);<a name="line.158"></a>
<FONT color="green">159</FONT>                    }<a name="line.159"></a>
<FONT color="green">160</FONT>                }<a name="line.160"></a>
<FONT color="green">161</FONT>    <a name="line.161"></a>
<FONT color="green">162</FONT>            }<a name="line.162"></a>
<FONT color="green">163</FONT>    <a name="line.163"></a>
<FONT color="green">164</FONT>        }<a name="line.164"></a>
<FONT color="green">165</FONT>    <a name="line.165"></a>
<FONT color="green">166</FONT>        /** {@inheritDoc} */<a name="line.166"></a>
<FONT color="green">167</FONT>        public abstract AbstractRegion&lt;S, T&gt; buildNew(BSPTree&lt;S&gt; newTree);<a name="line.167"></a>
<FONT color="green">168</FONT>    <a name="line.168"></a>
<FONT color="green">169</FONT>        /** Recursively build a tree by inserting cut sub-hyperplanes.<a name="line.169"></a>
<FONT color="green">170</FONT>         * @param node current tree node (it is a leaf node at the beginning<a name="line.170"></a>
<FONT color="green">171</FONT>         * of the call)<a name="line.171"></a>
<FONT color="green">172</FONT>         * @param boundary collection of edges belonging to the cell defined<a name="line.172"></a>
<FONT color="green">173</FONT>         * by the node<a name="line.173"></a>
<FONT color="green">174</FONT>         */<a name="line.174"></a>
<FONT color="green">175</FONT>        private void insertCuts(final BSPTree&lt;S&gt; node, final Collection&lt;SubHyperplane&lt;S&gt;&gt; boundary) {<a name="line.175"></a>
<FONT color="green">176</FONT>    <a name="line.176"></a>
<FONT color="green">177</FONT>            final Iterator&lt;SubHyperplane&lt;S&gt;&gt; iterator = boundary.iterator();<a name="line.177"></a>
<FONT color="green">178</FONT>    <a name="line.178"></a>
<FONT color="green">179</FONT>            // build the current level<a name="line.179"></a>
<FONT color="green">180</FONT>            Hyperplane&lt;S&gt; inserted = null;<a name="line.180"></a>
<FONT color="green">181</FONT>            while ((inserted == null) &amp;&amp; iterator.hasNext()) {<a name="line.181"></a>
<FONT color="green">182</FONT>                inserted = iterator.next().getHyperplane();<a name="line.182"></a>
<FONT color="green">183</FONT>                if (!node.insertCut(inserted.copySelf())) {<a name="line.183"></a>
<FONT color="green">184</FONT>                    inserted = null;<a name="line.184"></a>
<FONT color="green">185</FONT>                }<a name="line.185"></a>
<FONT color="green">186</FONT>            }<a name="line.186"></a>
<FONT color="green">187</FONT>    <a name="line.187"></a>
<FONT color="green">188</FONT>            if (!iterator.hasNext()) {<a name="line.188"></a>
<FONT color="green">189</FONT>                return;<a name="line.189"></a>
<FONT color="green">190</FONT>            }<a name="line.190"></a>
<FONT color="green">191</FONT>    <a name="line.191"></a>
<FONT color="green">192</FONT>            // distribute the remaining edges in the two sub-trees<a name="line.192"></a>
<FONT color="green">193</FONT>            final ArrayList&lt;SubHyperplane&lt;S&gt;&gt; plusList  = new ArrayList&lt;SubHyperplane&lt;S&gt;&gt;();<a name="line.193"></a>
<FONT color="green">194</FONT>            final ArrayList&lt;SubHyperplane&lt;S&gt;&gt; minusList = new ArrayList&lt;SubHyperplane&lt;S&gt;&gt;();<a name="line.194"></a>
<FONT color="green">195</FONT>            while (iterator.hasNext()) {<a name="line.195"></a>
<FONT color="green">196</FONT>                final SubHyperplane&lt;S&gt; other = iterator.next();<a name="line.196"></a>
<FONT color="green">197</FONT>                switch (other.side(inserted)) {<a name="line.197"></a>
<FONT color="green">198</FONT>                case PLUS:<a name="line.198"></a>
<FONT color="green">199</FONT>                    plusList.add(other);<a name="line.199"></a>
<FONT color="green">200</FONT>                    break;<a name="line.200"></a>
<FONT color="green">201</FONT>                case MINUS:<a name="line.201"></a>
<FONT color="green">202</FONT>                    minusList.add(other);<a name="line.202"></a>
<FONT color="green">203</FONT>                    break;<a name="line.203"></a>
<FONT color="green">204</FONT>                case BOTH:<a name="line.204"></a>
<FONT color="green">205</FONT>                    final SubHyperplane.SplitSubHyperplane&lt;S&gt; split = other.split(inserted);<a name="line.205"></a>
<FONT color="green">206</FONT>                    plusList.add(split.getPlus());<a name="line.206"></a>
<FONT color="green">207</FONT>                    minusList.add(split.getMinus());<a name="line.207"></a>
<FONT color="green">208</FONT>                    break;<a name="line.208"></a>
<FONT color="green">209</FONT>                default:<a name="line.209"></a>
<FONT color="green">210</FONT>                    // ignore the sub-hyperplanes belonging to the cut hyperplane<a name="line.210"></a>
<FONT color="green">211</FONT>                }<a name="line.211"></a>
<FONT color="green">212</FONT>            }<a name="line.212"></a>
<FONT color="green">213</FONT>    <a name="line.213"></a>
<FONT color="green">214</FONT>            // recurse through lower levels<a name="line.214"></a>
<FONT color="green">215</FONT>            insertCuts(node.getPlus(),  plusList);<a name="line.215"></a>
<FONT color="green">216</FONT>            insertCuts(node.getMinus(), minusList);<a name="line.216"></a>
<FONT color="green">217</FONT>    <a name="line.217"></a>
<FONT color="green">218</FONT>        }<a name="line.218"></a>
<FONT color="green">219</FONT>    <a name="line.219"></a>
<FONT color="green">220</FONT>        /** {@inheritDoc} */<a name="line.220"></a>
<FONT color="green">221</FONT>        public AbstractRegion&lt;S, T&gt; copySelf() {<a name="line.221"></a>
<FONT color="green">222</FONT>            return buildNew(tree.copySelf());<a name="line.222"></a>
<FONT color="green">223</FONT>        }<a name="line.223"></a>
<FONT color="green">224</FONT>    <a name="line.224"></a>
<FONT color="green">225</FONT>        /** {@inheritDoc} */<a name="line.225"></a>
<FONT color="green">226</FONT>        public boolean isEmpty() {<a name="line.226"></a>
<FONT color="green">227</FONT>            return isEmpty(tree);<a name="line.227"></a>
<FONT color="green">228</FONT>        }<a name="line.228"></a>
<FONT color="green">229</FONT>    <a name="line.229"></a>
<FONT color="green">230</FONT>        /** {@inheritDoc} */<a name="line.230"></a>
<FONT color="green">231</FONT>        public boolean isEmpty(final BSPTree&lt;S&gt; node) {<a name="line.231"></a>
<FONT color="green">232</FONT>    <a name="line.232"></a>
<FONT color="green">233</FONT>            // we use a recursive function rather than the BSPTreeVisitor<a name="line.233"></a>
<FONT color="green">234</FONT>            // interface because we can stop visiting the tree as soon as we<a name="line.234"></a>
<FONT color="green">235</FONT>            // have found an inside cell<a name="line.235"></a>
<FONT color="green">236</FONT>    <a name="line.236"></a>
<FONT color="green">237</FONT>            if (node.getCut() == null) {<a name="line.237"></a>
<FONT color="green">238</FONT>                // if we find an inside node, the region is not empty<a name="line.238"></a>
<FONT color="green">239</FONT>                return !((Boolean) node.getAttribute());<a name="line.239"></a>
<FONT color="green">240</FONT>            }<a name="line.240"></a>
<FONT color="green">241</FONT>    <a name="line.241"></a>
<FONT color="green">242</FONT>            // check both sides of the sub-tree<a name="line.242"></a>
<FONT color="green">243</FONT>            return isEmpty(node.getMinus()) &amp;&amp; isEmpty(node.getPlus());<a name="line.243"></a>
<FONT color="green">244</FONT>    <a name="line.244"></a>
<FONT color="green">245</FONT>        }<a name="line.245"></a>
<FONT color="green">246</FONT>    <a name="line.246"></a>
<FONT color="green">247</FONT>        /** {@inheritDoc} */<a name="line.247"></a>
<FONT color="green">248</FONT>        public boolean contains(final Region&lt;S&gt; region) {<a name="line.248"></a>
<FONT color="green">249</FONT>            return new RegionFactory&lt;S&gt;().difference(region, this).isEmpty();<a name="line.249"></a>
<FONT color="green">250</FONT>        }<a name="line.250"></a>
<FONT color="green">251</FONT>    <a name="line.251"></a>
<FONT color="green">252</FONT>        /** {@inheritDoc} */<a name="line.252"></a>
<FONT color="green">253</FONT>        public Location checkPoint(final Vector&lt;S&gt; point) {<a name="line.253"></a>
<FONT color="green">254</FONT>            return checkPoint(tree, point);<a name="line.254"></a>
<FONT color="green">255</FONT>        }<a name="line.255"></a>
<FONT color="green">256</FONT>    <a name="line.256"></a>
<FONT color="green">257</FONT>        /** Check a point with respect to the region starting at a given node.<a name="line.257"></a>
<FONT color="green">258</FONT>         * @param node root node of the region<a name="line.258"></a>
<FONT color="green">259</FONT>         * @param point point to check<a name="line.259"></a>
<FONT color="green">260</FONT>         * @return a code representing the point status: either {@link<a name="line.260"></a>
<FONT color="green">261</FONT>         * Region.Location#INSIDE INSIDE}, {@link Region.Location#OUTSIDE<a name="line.261"></a>
<FONT color="green">262</FONT>         * OUTSIDE} or {@link Region.Location#BOUNDARY BOUNDARY}<a name="line.262"></a>
<FONT color="green">263</FONT>         */<a name="line.263"></a>
<FONT color="green">264</FONT>        protected Location checkPoint(final BSPTree&lt;S&gt; node, final Vector&lt;S&gt; point) {<a name="line.264"></a>
<FONT color="green">265</FONT>            final BSPTree&lt;S&gt; cell = node.getCell(point);<a name="line.265"></a>
<FONT color="green">266</FONT>            if (cell.getCut() == null) {<a name="line.266"></a>
<FONT color="green">267</FONT>                // the point is in the interior of a cell, just check the attribute<a name="line.267"></a>
<FONT color="green">268</FONT>                return ((Boolean) cell.getAttribute()) ? Location.INSIDE : Location.OUTSIDE;<a name="line.268"></a>
<FONT color="green">269</FONT>            }<a name="line.269"></a>
<FONT color="green">270</FONT>    <a name="line.270"></a>
<FONT color="green">271</FONT>            // the point is on a cut-sub-hyperplane, is it on a boundary ?<a name="line.271"></a>
<FONT color="green">272</FONT>            final Location minusCode = checkPoint(cell.getMinus(), point);<a name="line.272"></a>
<FONT color="green">273</FONT>            final Location plusCode  = checkPoint(cell.getPlus(),  point);<a name="line.273"></a>
<FONT color="green">274</FONT>            return (minusCode == plusCode) ? minusCode : Location.BOUNDARY;<a name="line.274"></a>
<FONT color="green">275</FONT>    <a name="line.275"></a>
<FONT color="green">276</FONT>        }<a name="line.276"></a>
<FONT color="green">277</FONT>    <a name="line.277"></a>
<FONT color="green">278</FONT>        /** {@inheritDoc} */<a name="line.278"></a>
<FONT color="green">279</FONT>        public BSPTree&lt;S&gt; getTree(final boolean includeBoundaryAttributes) {<a name="line.279"></a>
<FONT color="green">280</FONT>            if (includeBoundaryAttributes &amp;&amp; (tree.getCut() != null) &amp;&amp; (tree.getAttribute() == null)) {<a name="line.280"></a>
<FONT color="green">281</FONT>                // we need to compute the boundary attributes<a name="line.281"></a>
<FONT color="green">282</FONT>                tree.visit(new BoundaryBuilder&lt;S&gt;());<a name="line.282"></a>
<FONT color="green">283</FONT>            }<a name="line.283"></a>
<FONT color="green">284</FONT>            return tree;<a name="line.284"></a>
<FONT color="green">285</FONT>        }<a name="line.285"></a>
<FONT color="green">286</FONT>    <a name="line.286"></a>
<FONT color="green">287</FONT>        /** Visitor building boundary shell tree.<a name="line.287"></a>
<FONT color="green">288</FONT>         * &lt;p&gt;<a name="line.288"></a>
<FONT color="green">289</FONT>         * The boundary shell is represented as {@link BoundaryAttribute boundary attributes}<a name="line.289"></a>
<FONT color="green">290</FONT>         * at each internal node.<a name="line.290"></a>
<FONT color="green">291</FONT>         * &lt;/p&gt;<a name="line.291"></a>
<FONT color="green">292</FONT>         */<a name="line.292"></a>
<FONT color="green">293</FONT>        private static class BoundaryBuilder&lt;S extends Space&gt; implements BSPTreeVisitor&lt;S&gt; {<a name="line.293"></a>
<FONT color="green">294</FONT>    <a name="line.294"></a>
<FONT color="green">295</FONT>            /** {@inheritDoc} */<a name="line.295"></a>
<FONT color="green">296</FONT>            public Order visitOrder(BSPTree&lt;S&gt; node) {<a name="line.296"></a>
<FONT color="green">297</FONT>                return Order.PLUS_MINUS_SUB;<a name="line.297"></a>
<FONT color="green">298</FONT>            }<a name="line.298"></a>
<FONT color="green">299</FONT>    <a name="line.299"></a>
<FONT color="green">300</FONT>            /** {@inheritDoc} */<a name="line.300"></a>
<FONT color="green">301</FONT>            public void visitInternalNode(BSPTree&lt;S&gt; node) {<a name="line.301"></a>
<FONT color="green">302</FONT>    <a name="line.302"></a>
<FONT color="green">303</FONT>                SubHyperplane&lt;S&gt; plusOutside = null;<a name="line.303"></a>
<FONT color="green">304</FONT>                SubHyperplane&lt;S&gt; plusInside  = null;<a name="line.304"></a>
<FONT color="green">305</FONT>    <a name="line.305"></a>
<FONT color="green">306</FONT>                // characterize the cut sub-hyperplane,<a name="line.306"></a>
<FONT color="green">307</FONT>                // first with respect to the plus sub-tree<a name="line.307"></a>
<FONT color="green">308</FONT>                @SuppressWarnings("unchecked")<a name="line.308"></a>
<FONT color="green">309</FONT>                final SubHyperplane&lt;S&gt;[] plusChar = (SubHyperplane&lt;S&gt;[]) Array.newInstance(SubHyperplane.class, 2);<a name="line.309"></a>
<FONT color="green">310</FONT>                characterize(node.getPlus(), node.getCut().copySelf(), plusChar);<a name="line.310"></a>
<FONT color="green">311</FONT>    <a name="line.311"></a>
<FONT color="green">312</FONT>                if (plusChar[0] != null &amp;&amp; !plusChar[0].isEmpty()) {<a name="line.312"></a>
<FONT color="green">313</FONT>                    // plusChar[0] corresponds to a subset of the cut sub-hyperplane known to have<a name="line.313"></a>
<FONT color="green">314</FONT>                    // outside cells on its plus side, we want to check if parts of this subset<a name="line.314"></a>
<FONT color="green">315</FONT>                    // do have inside cells on their minus side<a name="line.315"></a>
<FONT color="green">316</FONT>                    @SuppressWarnings("unchecked")<a name="line.316"></a>
<FONT color="green">317</FONT>                    final SubHyperplane&lt;S&gt;[] minusChar = (SubHyperplane&lt;S&gt;[]) Array.newInstance(SubHyperplane.class, 2);<a name="line.317"></a>
<FONT color="green">318</FONT>                    characterize(node.getMinus(), plusChar[0], minusChar);<a name="line.318"></a>
<FONT color="green">319</FONT>                    if (minusChar[1] != null &amp;&amp; !minusChar[1].isEmpty()) {<a name="line.319"></a>
<FONT color="green">320</FONT>                        // this part belongs to the boundary,<a name="line.320"></a>
<FONT color="green">321</FONT>                        // it has the outside on its plus side and the inside on its minus side<a name="line.321"></a>
<FONT color="green">322</FONT>                        plusOutside = minusChar[1];<a name="line.322"></a>
<FONT color="green">323</FONT>                    }<a name="line.323"></a>
<FONT color="green">324</FONT>                }<a name="line.324"></a>
<FONT color="green">325</FONT>    <a name="line.325"></a>
<FONT color="green">326</FONT>                if (plusChar[1] != null &amp;&amp; !plusChar[1].isEmpty()) {<a name="line.326"></a>
<FONT color="green">327</FONT>                    // plusChar[1] corresponds to a subset of the cut sub-hyperplane known to have<a name="line.327"></a>
<FONT color="green">328</FONT>                    // inside cells on its plus side, we want to check if parts of this subset<a name="line.328"></a>
<FONT color="green">329</FONT>                    // do have outside cells on their minus side<a name="line.329"></a>
<FONT color="green">330</FONT>                    @SuppressWarnings("unchecked")<a name="line.330"></a>
<FONT color="green">331</FONT>                    final SubHyperplane&lt;S&gt;[] minusChar = (SubHyperplane&lt;S&gt;[]) Array.newInstance(SubHyperplane.class, 2);<a name="line.331"></a>
<FONT color="green">332</FONT>                    characterize(node.getMinus(), plusChar[1], minusChar);<a name="line.332"></a>
<FONT color="green">333</FONT>                    if (minusChar[0] != null &amp;&amp; !minusChar[0].isEmpty()) {<a name="line.333"></a>
<FONT color="green">334</FONT>                        // this part belongs to the boundary,<a name="line.334"></a>
<FONT color="green">335</FONT>                        // it has the inside on its plus side and the outside on its minus side<a name="line.335"></a>
<FONT color="green">336</FONT>                        plusInside = minusChar[0];<a name="line.336"></a>
<FONT color="green">337</FONT>                    }<a name="line.337"></a>
<FONT color="green">338</FONT>                }<a name="line.338"></a>
<FONT color="green">339</FONT>    <a name="line.339"></a>
<FONT color="green">340</FONT>                // set the boundary attribute at non-leaf nodes<a name="line.340"></a>
<FONT color="green">341</FONT>                node.setAttribute(new BoundaryAttribute&lt;S&gt;(plusOutside, plusInside));<a name="line.341"></a>
<FONT color="green">342</FONT>    <a name="line.342"></a>
<FONT color="green">343</FONT>            }<a name="line.343"></a>
<FONT color="green">344</FONT>    <a name="line.344"></a>
<FONT color="green">345</FONT>            /** {@inheritDoc} */<a name="line.345"></a>
<FONT color="green">346</FONT>            public void visitLeafNode(BSPTree&lt;S&gt; node) {<a name="line.346"></a>
<FONT color="green">347</FONT>            }<a name="line.347"></a>
<FONT color="green">348</FONT>    <a name="line.348"></a>
<FONT color="green">349</FONT>            /** Filter the parts of an hyperplane belonging to the boundary.<a name="line.349"></a>
<FONT color="green">350</FONT>             * &lt;p&gt;The filtering consist in splitting the specified<a name="line.350"></a>
<FONT color="green">351</FONT>             * sub-hyperplane into several parts lying in inside and outside<a name="line.351"></a>
<FONT color="green">352</FONT>             * cells of the tree. The principle is to call this method twice for<a name="line.352"></a>
<FONT color="green">353</FONT>             * each cut sub-hyperplane in the tree, once one the plus node and<a name="line.353"></a>
<FONT color="green">354</FONT>             * once on the minus node. The parts that have the same flag<a name="line.354"></a>
<FONT color="green">355</FONT>             * (inside/inside or outside/outside) do not belong to the boundary<a name="line.355"></a>
<FONT color="green">356</FONT>             * while parts that have different flags (inside/outside or<a name="line.356"></a>
<FONT color="green">357</FONT>             * outside/inside) do belong to the boundary.&lt;/p&gt;<a name="line.357"></a>
<FONT color="green">358</FONT>             * @param node current BSP tree node<a name="line.358"></a>
<FONT color="green">359</FONT>             * @param sub sub-hyperplane to characterize<a name="line.359"></a>
<FONT color="green">360</FONT>             * @param characterization placeholder where to put the characterized parts<a name="line.360"></a>
<FONT color="green">361</FONT>             */<a name="line.361"></a>
<FONT color="green">362</FONT>            private void characterize(final BSPTree&lt;S&gt; node, final SubHyperplane&lt;S&gt; sub,<a name="line.362"></a>
<FONT color="green">363</FONT>                                      final SubHyperplane&lt;S&gt;[] characterization) {<a name="line.363"></a>
<FONT color="green">364</FONT>                if (node.getCut() == null) {<a name="line.364"></a>
<FONT color="green">365</FONT>                    // we have reached a leaf node<a name="line.365"></a>
<FONT color="green">366</FONT>                    final boolean inside = (Boolean) node.getAttribute();<a name="line.366"></a>
<FONT color="green">367</FONT>                    if (inside) {<a name="line.367"></a>
<FONT color="green">368</FONT>                        if (characterization[1] == null) {<a name="line.368"></a>
<FONT color="green">369</FONT>                            characterization[1] = sub;<a name="line.369"></a>
<FONT color="green">370</FONT>                        } else {<a name="line.370"></a>
<FONT color="green">371</FONT>                            characterization[1] = characterization[1].reunite(sub);<a name="line.371"></a>
<FONT color="green">372</FONT>                        }<a name="line.372"></a>
<FONT color="green">373</FONT>                    } else {<a name="line.373"></a>
<FONT color="green">374</FONT>                        if (characterization[0] == null) {<a name="line.374"></a>
<FONT color="green">375</FONT>                            characterization[0] = sub;<a name="line.375"></a>
<FONT color="green">376</FONT>                        } else {<a name="line.376"></a>
<FONT color="green">377</FONT>                            characterization[0] = characterization[0].reunite(sub);<a name="line.377"></a>
<FONT color="green">378</FONT>                        }<a name="line.378"></a>
<FONT color="green">379</FONT>                    }<a name="line.379"></a>
<FONT color="green">380</FONT>                } else {<a name="line.380"></a>
<FONT color="green">381</FONT>                    final Hyperplane&lt;S&gt; hyperplane = node.getCut().getHyperplane();<a name="line.381"></a>
<FONT color="green">382</FONT>                    switch (sub.side(hyperplane)) {<a name="line.382"></a>
<FONT color="green">383</FONT>                    case PLUS:<a name="line.383"></a>
<FONT color="green">384</FONT>                        characterize(node.getPlus(), sub, characterization);<a name="line.384"></a>
<FONT color="green">385</FONT>                        break;<a name="line.385"></a>
<FONT color="green">386</FONT>                    case MINUS:<a name="line.386"></a>
<FONT color="green">387</FONT>                        characterize(node.getMinus(), sub, characterization);<a name="line.387"></a>
<FONT color="green">388</FONT>                        break;<a name="line.388"></a>
<FONT color="green">389</FONT>                    case BOTH:<a name="line.389"></a>
<FONT color="green">390</FONT>                        final SubHyperplane.SplitSubHyperplane&lt;S&gt; split = sub.split(hyperplane);<a name="line.390"></a>
<FONT color="green">391</FONT>                        characterize(node.getPlus(),  split.getPlus(),  characterization);<a name="line.391"></a>
<FONT color="green">392</FONT>                        characterize(node.getMinus(), split.getMinus(), characterization);<a name="line.392"></a>
<FONT color="green">393</FONT>                        break;<a name="line.393"></a>
<FONT color="green">394</FONT>                    default:<a name="line.394"></a>
<FONT color="green">395</FONT>                        // this should not happen<a name="line.395"></a>
<FONT color="green">396</FONT>                        throw new MathInternalError();<a name="line.396"></a>
<FONT color="green">397</FONT>                    }<a name="line.397"></a>
<FONT color="green">398</FONT>                }<a name="line.398"></a>
<FONT color="green">399</FONT>            }<a name="line.399"></a>
<FONT color="green">400</FONT>    <a name="line.400"></a>
<FONT color="green">401</FONT>        }<a name="line.401"></a>
<FONT color="green">402</FONT>    <a name="line.402"></a>
<FONT color="green">403</FONT>        /** {@inheritDoc} */<a name="line.403"></a>
<FONT color="green">404</FONT>        public double getBoundarySize() {<a name="line.404"></a>
<FONT color="green">405</FONT>            final BoundarySizeVisitor&lt;S&gt; visitor = new BoundarySizeVisitor&lt;S&gt;();<a name="line.405"></a>
<FONT color="green">406</FONT>            getTree(true).visit(visitor);<a name="line.406"></a>
<FONT color="green">407</FONT>            return visitor.getSize();<a name="line.407"></a>
<FONT color="green">408</FONT>        }<a name="line.408"></a>
<FONT color="green">409</FONT>    <a name="line.409"></a>
<FONT color="green">410</FONT>        /** {@inheritDoc} */<a name="line.410"></a>
<FONT color="green">411</FONT>        public double getSize() {<a name="line.411"></a>
<FONT color="green">412</FONT>            if (barycenter == null) {<a name="line.412"></a>
<FONT color="green">413</FONT>                computeGeometricalProperties();<a name="line.413"></a>
<FONT color="green">414</FONT>            }<a name="line.414"></a>
<FONT color="green">415</FONT>            return size;<a name="line.415"></a>
<FONT color="green">416</FONT>        }<a name="line.416"></a>
<FONT color="green">417</FONT>    <a name="line.417"></a>
<FONT color="green">418</FONT>        /** Set the size of the instance.<a name="line.418"></a>
<FONT color="green">419</FONT>         * @param size size of the instance<a name="line.419"></a>
<FONT color="green">420</FONT>         */<a name="line.420"></a>
<FONT color="green">421</FONT>        protected void setSize(final double size) {<a name="line.421"></a>
<FONT color="green">422</FONT>            this.size = size;<a name="line.422"></a>
<FONT color="green">423</FONT>        }<a name="line.423"></a>
<FONT color="green">424</FONT>    <a name="line.424"></a>
<FONT color="green">425</FONT>        /** {@inheritDoc} */<a name="line.425"></a>
<FONT color="green">426</FONT>        public Vector&lt;S&gt; getBarycenter() {<a name="line.426"></a>
<FONT color="green">427</FONT>            if (barycenter == null) {<a name="line.427"></a>
<FONT color="green">428</FONT>                computeGeometricalProperties();<a name="line.428"></a>
<FONT color="green">429</FONT>            }<a name="line.429"></a>
<FONT color="green">430</FONT>            return barycenter;<a name="line.430"></a>
<FONT color="green">431</FONT>        }<a name="line.431"></a>
<FONT color="green">432</FONT>    <a name="line.432"></a>
<FONT color="green">433</FONT>        /** Set the barycenter of the instance.<a name="line.433"></a>
<FONT color="green">434</FONT>         * @param barycenter barycenter of the instance<a name="line.434"></a>
<FONT color="green">435</FONT>         */<a name="line.435"></a>
<FONT color="green">436</FONT>        protected void setBarycenter(final Vector&lt;S&gt; barycenter) {<a name="line.436"></a>
<FONT color="green">437</FONT>            this.barycenter = barycenter;<a name="line.437"></a>
<FONT color="green">438</FONT>        }<a name="line.438"></a>
<FONT color="green">439</FONT>    <a name="line.439"></a>
<FONT color="green">440</FONT>        /** Compute some geometrical properties.<a name="line.440"></a>
<FONT color="green">441</FONT>         * &lt;p&gt;The properties to compute are the barycenter and the size.&lt;/p&gt;<a name="line.441"></a>
<FONT color="green">442</FONT>         */<a name="line.442"></a>
<FONT color="green">443</FONT>        protected abstract void computeGeometricalProperties();<a name="line.443"></a>
<FONT color="green">444</FONT>    <a name="line.444"></a>
<FONT color="green">445</FONT>        /** {@inheritDoc} */<a name="line.445"></a>
<FONT color="green">446</FONT>        public Side side(final Hyperplane&lt;S&gt; hyperplane) {<a name="line.446"></a>
<FONT color="green">447</FONT>            final Sides sides = new Sides();<a name="line.447"></a>
<FONT color="green">448</FONT>            recurseSides(tree, hyperplane.wholeHyperplane(), sides);<a name="line.448"></a>
<FONT color="green">449</FONT>            return sides.plusFound() ?<a name="line.449"></a>
<FONT color="green">450</FONT>                  (sides.minusFound() ? Side.BOTH  : Side.PLUS) :<a name="line.450"></a>
<FONT color="green">451</FONT>                  (sides.minusFound() ? Side.MINUS : Side.HYPER);<a name="line.451"></a>
<FONT color="green">452</FONT>        }<a name="line.452"></a>
<FONT color="green">453</FONT>    <a name="line.453"></a>
<FONT color="green">454</FONT>        /** Search recursively for inside leaf nodes on each side of the given hyperplane.<a name="line.454"></a>
<FONT color="green">455</FONT>    <a name="line.455"></a>
<FONT color="green">456</FONT>         * &lt;p&gt;The algorithm used here is directly derived from the one<a name="line.456"></a>
<FONT color="green">457</FONT>         * described in section III (&lt;i&gt;Binary Partitioning of a BSP<a name="line.457"></a>
<FONT color="green">458</FONT>         * Tree&lt;/i&gt;) of the Bruce Naylor, John Amanatides and William<a name="line.458"></a>
<FONT color="green">459</FONT>         * Thibault paper &lt;a<a name="line.459"></a>
<FONT color="green">460</FONT>         * href="http://www.cs.yorku.ca/~amana/research/bsptSetOp.pdf"&gt;Merging<a name="line.460"></a>
<FONT color="green">461</FONT>         * BSP Trees Yields Polyhedral Set Operations&lt;/a&gt; Proc. Siggraph<a name="line.461"></a>
<FONT color="green">462</FONT>         * '90, Computer Graphics 24(4), August 1990, pp 115-124, published<a name="line.462"></a>
<FONT color="green">463</FONT>         * by the Association for Computing Machinery (ACM)..&lt;/p&gt;<a name="line.463"></a>
<FONT color="green">464</FONT>    <a name="line.464"></a>
<FONT color="green">465</FONT>         * @param node current BSP tree node<a name="line.465"></a>
<FONT color="green">466</FONT>         * @param sub sub-hyperplane<a name="line.466"></a>
<FONT color="green">467</FONT>         * @param sides object holding the sides found<a name="line.467"></a>
<FONT color="green">468</FONT>         */<a name="line.468"></a>
<FONT color="green">469</FONT>        private void recurseSides(final BSPTree&lt;S&gt; node, final SubHyperplane&lt;S&gt; sub, final Sides sides) {<a name="line.469"></a>
<FONT color="green">470</FONT>    <a name="line.470"></a>
<FONT color="green">471</FONT>            if (node.getCut() == null) {<a name="line.471"></a>
<FONT color="green">472</FONT>                if ((Boolean) node.getAttribute()) {<a name="line.472"></a>
<FONT color="green">473</FONT>                    // this is an inside cell expanding across the hyperplane<a name="line.473"></a>
<FONT color="green">474</FONT>                    sides.rememberPlusFound();<a name="line.474"></a>
<FONT color="green">475</FONT>                    sides.rememberMinusFound();<a name="line.475"></a>
<FONT color="green">476</FONT>                }<a name="line.476"></a>
<FONT color="green">477</FONT>                return;<a name="line.477"></a>
<FONT color="green">478</FONT>            }<a name="line.478"></a>
<FONT color="green">479</FONT>    <a name="line.479"></a>
<FONT color="green">480</FONT>            final Hyperplane&lt;S&gt; hyperplane = node.getCut().getHyperplane();<a name="line.480"></a>
<FONT color="green">481</FONT>            switch (sub.side(hyperplane)) {<a name="line.481"></a>
<FONT color="green">482</FONT>            case PLUS :<a name="line.482"></a>
<FONT color="green">483</FONT>                // the sub-hyperplane is entirely in the plus sub-tree<a name="line.483"></a>
<FONT color="green">484</FONT>                if (node.getCut().side(sub.getHyperplane()) == Side.PLUS) {<a name="line.484"></a>
<FONT color="green">485</FONT>                    if (!isEmpty(node.getMinus())) {<a name="line.485"></a>
<FONT color="green">486</FONT>                        sides.rememberPlusFound();<a name="line.486"></a>
<FONT color="green">487</FONT>                    }<a name="line.487"></a>
<FONT color="green">488</FONT>                } else {<a name="line.488"></a>
<FONT color="green">489</FONT>                    if (!isEmpty(node.getMinus())) {<a name="line.489"></a>
<FONT color="green">490</FONT>                        sides.rememberMinusFound();<a name="line.490"></a>
<FONT color="green">491</FONT>                    }<a name="line.491"></a>
<FONT color="green">492</FONT>                }<a name="line.492"></a>
<FONT color="green">493</FONT>                if (!(sides.plusFound() &amp;&amp; sides.minusFound())) {<a name="line.493"></a>
<FONT color="green">494</FONT>                    recurseSides(node.getPlus(), sub, sides);<a name="line.494"></a>
<FONT color="green">495</FONT>                }<a name="line.495"></a>
<FONT color="green">496</FONT>                break;<a name="line.496"></a>
<FONT color="green">497</FONT>            case MINUS :<a name="line.497"></a>
<FONT color="green">498</FONT>                // the sub-hyperplane is entirely in the minus sub-tree<a name="line.498"></a>
<FONT color="green">499</FONT>                if (node.getCut().side(sub.getHyperplane()) == Side.PLUS) {<a name="line.499"></a>
<FONT color="green">500</FONT>                    if (!isEmpty(node.getPlus())) {<a name="line.500"></a>
<FONT color="green">501</FONT>                        sides.rememberPlusFound();<a name="line.501"></a>
<FONT color="green">502</FONT>                    }<a name="line.502"></a>
<FONT color="green">503</FONT>                } else {<a name="line.503"></a>
<FONT color="green">504</FONT>                    if (!isEmpty(node.getPlus())) {<a name="line.504"></a>
<FONT color="green">505</FONT>                        sides.rememberMinusFound();<a name="line.505"></a>
<FONT color="green">506</FONT>                    }<a name="line.506"></a>
<FONT color="green">507</FONT>                }<a name="line.507"></a>
<FONT color="green">508</FONT>                if (!(sides.plusFound() &amp;&amp; sides.minusFound())) {<a name="line.508"></a>
<FONT color="green">509</FONT>                    recurseSides(node.getMinus(), sub, sides);<a name="line.509"></a>
<FONT color="green">510</FONT>                }<a name="line.510"></a>
<FONT color="green">511</FONT>                break;<a name="line.511"></a>
<FONT color="green">512</FONT>            case BOTH :<a name="line.512"></a>
<FONT color="green">513</FONT>                // the sub-hyperplane extends in both sub-trees<a name="line.513"></a>
<FONT color="green">514</FONT>                final SubHyperplane.SplitSubHyperplane&lt;S&gt; split = sub.split(hyperplane);<a name="line.514"></a>
<FONT color="green">515</FONT>    <a name="line.515"></a>
<FONT color="green">516</FONT>                // explore first the plus sub-tree<a name="line.516"></a>
<FONT color="green">517</FONT>                recurseSides(node.getPlus(), split.getPlus(), sides);<a name="line.517"></a>
<FONT color="green">518</FONT>    <a name="line.518"></a>
<FONT color="green">519</FONT>                // if needed, explore the minus sub-tree<a name="line.519"></a>
<FONT color="green">520</FONT>                if (!(sides.plusFound() &amp;&amp; sides.minusFound())) {<a name="line.520"></a>
<FONT color="green">521</FONT>                    recurseSides(node.getMinus(), split.getMinus(), sides);<a name="line.521"></a>
<FONT color="green">522</FONT>                }<a name="line.522"></a>
<FONT color="green">523</FONT>                break;<a name="line.523"></a>
<FONT color="green">524</FONT>            default :<a name="line.524"></a>
<FONT color="green">525</FONT>                // the sub-hyperplane and the cut sub-hyperplane share the same hyperplane<a name="line.525"></a>
<FONT color="green">526</FONT>                if (node.getCut().getHyperplane().sameOrientationAs(sub.getHyperplane())) {<a name="line.526"></a>
<FONT color="green">527</FONT>                    if ((node.getPlus().getCut() != null) || ((Boolean) node.getPlus().getAttribute())) {<a name="line.527"></a>
<FONT color="green">528</FONT>                        sides.rememberPlusFound();<a name="line.528"></a>
<FONT color="green">529</FONT>                    }<a name="line.529"></a>
<FONT color="green">530</FONT>                    if ((node.getMinus().getCut() != null) || ((Boolean) node.getMinus().getAttribute())) {<a name="line.530"></a>
<FONT color="green">531</FONT>                        sides.rememberMinusFound();<a name="line.531"></a>
<FONT color="green">532</FONT>                    }<a name="line.532"></a>
<FONT color="green">533</FONT>                } else {<a name="line.533"></a>
<FONT color="green">534</FONT>                    if ((node.getPlus().getCut() != null) || ((Boolean) node.getPlus().getAttribute())) {<a name="line.534"></a>
<FONT color="green">535</FONT>                        sides.rememberMinusFound();<a name="line.535"></a>
<FONT color="green">536</FONT>                    }<a name="line.536"></a>
<FONT color="green">537</FONT>                    if ((node.getMinus().getCut() != null) || ((Boolean) node.getMinus().getAttribute())) {<a name="line.537"></a>
<FONT color="green">538</FONT>                        sides.rememberPlusFound();<a name="line.538"></a>
<FONT color="green">539</FONT>                    }<a name="line.539"></a>
<FONT color="green">540</FONT>                }<a name="line.540"></a>
<FONT color="green">541</FONT>            }<a name="line.541"></a>
<FONT color="green">542</FONT>    <a name="line.542"></a>
<FONT color="green">543</FONT>        }<a name="line.543"></a>
<FONT color="green">544</FONT>    <a name="line.544"></a>
<FONT color="green">545</FONT>        /** Utility class holding the already found sides. */<a name="line.545"></a>
<FONT color="green">546</FONT>        private static final class Sides {<a name="line.546"></a>
<FONT color="green">547</FONT>    <a name="line.547"></a>
<FONT color="green">548</FONT>            /** Indicator of inside leaf nodes found on the plus side. */<a name="line.548"></a>
<FONT color="green">549</FONT>            private boolean plusFound;<a name="line.549"></a>
<FONT color="green">550</FONT>    <a name="line.550"></a>
<FONT color="green">551</FONT>            /** Indicator of inside leaf nodes found on the plus side. */<a name="line.551"></a>
<FONT color="green">552</FONT>            private boolean minusFound;<a name="line.552"></a>
<FONT color="green">553</FONT>    <a name="line.553"></a>
<FONT color="green">554</FONT>            /** Simple constructor.<a name="line.554"></a>
<FONT color="green">555</FONT>             */<a name="line.555"></a>
<FONT color="green">556</FONT>            public Sides() {<a name="line.556"></a>
<FONT color="green">557</FONT>                plusFound  = false;<a name="line.557"></a>
<FONT color="green">558</FONT>                minusFound = false;<a name="line.558"></a>
<FONT color="green">559</FONT>            }<a name="line.559"></a>
<FONT color="green">560</FONT>    <a name="line.560"></a>
<FONT color="green">561</FONT>            /** Remember the fact that inside leaf nodes have been found on the plus side.<a name="line.561"></a>
<FONT color="green">562</FONT>             */<a name="line.562"></a>
<FONT color="green">563</FONT>            public void rememberPlusFound() {<a name="line.563"></a>
<FONT color="green">564</FONT>                plusFound = true;<a name="line.564"></a>
<FONT color="green">565</FONT>            }<a name="line.565"></a>
<FONT color="green">566</FONT>    <a name="line.566"></a>
<FONT color="green">567</FONT>            /** Check if inside leaf nodes have been found on the plus side.<a name="line.567"></a>
<FONT color="green">568</FONT>             * @return true if inside leaf nodes have been found on the plus side<a name="line.568"></a>
<FONT color="green">569</FONT>             */<a name="line.569"></a>
<FONT color="green">570</FONT>            public boolean plusFound() {<a name="line.570"></a>
<FONT color="green">571</FONT>                return plusFound;<a name="line.571"></a>
<FONT color="green">572</FONT>            }<a name="line.572"></a>
<FONT color="green">573</FONT>    <a name="line.573"></a>
<FONT color="green">574</FONT>            /** Remember the fact that inside leaf nodes have been found on the minus side.<a name="line.574"></a>
<FONT color="green">575</FONT>             */<a name="line.575"></a>
<FONT color="green">576</FONT>            public void rememberMinusFound() {<a name="line.576"></a>
<FONT color="green">577</FONT>                minusFound = true;<a name="line.577"></a>
<FONT color="green">578</FONT>            }<a name="line.578"></a>
<FONT color="green">579</FONT>    <a name="line.579"></a>
<FONT color="green">580</FONT>            /** Check if inside leaf nodes have been found on the minus side.<a name="line.580"></a>
<FONT color="green">581</FONT>             * @return true if inside leaf nodes have been found on the minus side<a name="line.581"></a>
<FONT color="green">582</FONT>             */<a name="line.582"></a>
<FONT color="green">583</FONT>            public boolean minusFound() {<a name="line.583"></a>
<FONT color="green">584</FONT>                return minusFound;<a name="line.584"></a>
<FONT color="green">585</FONT>            }<a name="line.585"></a>
<FONT color="green">586</FONT>    <a name="line.586"></a>
<FONT color="green">587</FONT>        }<a name="line.587"></a>
<FONT color="green">588</FONT>    <a name="line.588"></a>
<FONT color="green">589</FONT>        /** {@inheritDoc} */<a name="line.589"></a>
<FONT color="green">590</FONT>        public SubHyperplane&lt;S&gt; intersection(final SubHyperplane&lt;S&gt; sub) {<a name="line.590"></a>
<FONT color="green">591</FONT>            return recurseIntersection(tree, sub);<a name="line.591"></a>
<FONT color="green">592</FONT>        }<a name="line.592"></a>
<FONT color="green">593</FONT>    <a name="line.593"></a>
<FONT color="green">594</FONT>        /** Recursively compute the parts of a sub-hyperplane that are<a name="line.594"></a>
<FONT color="green">595</FONT>         * contained in the region.<a name="line.595"></a>
<FONT color="green">596</FONT>         * @param node current BSP tree node<a name="line.596"></a>
<FONT color="green">597</FONT>         * @param sub sub-hyperplane traversing the region<a name="line.597"></a>
<FONT color="green">598</FONT>         * @return filtered sub-hyperplane<a name="line.598"></a>
<FONT color="green">599</FONT>         */<a name="line.599"></a>
<FONT color="green">600</FONT>        private SubHyperplane&lt;S&gt; recurseIntersection(final BSPTree&lt;S&gt; node, final SubHyperplane&lt;S&gt; sub) {<a name="line.600"></a>
<FONT color="green">601</FONT>    <a name="line.601"></a>
<FONT color="green">602</FONT>            if (node.getCut() == null) {<a name="line.602"></a>
<FONT color="green">603</FONT>                return (Boolean) node.getAttribute() ? sub.copySelf() : null;<a name="line.603"></a>
<FONT color="green">604</FONT>            }<a name="line.604"></a>
<FONT color="green">605</FONT>    <a name="line.605"></a>
<FONT color="green">606</FONT>            final Hyperplane&lt;S&gt; hyperplane = node.getCut().getHyperplane();<a name="line.606"></a>
<FONT color="green">607</FONT>            switch (sub.side(hyperplane)) {<a name="line.607"></a>
<FONT color="green">608</FONT>            case PLUS :<a name="line.608"></a>
<FONT color="green">609</FONT>                return recurseIntersection(node.getPlus(), sub);<a name="line.609"></a>
<FONT color="green">610</FONT>            case MINUS :<a name="line.610"></a>
<FONT color="green">611</FONT>                return recurseIntersection(node.getMinus(), sub);<a name="line.611"></a>
<FONT color="green">612</FONT>            case BOTH :<a name="line.612"></a>
<FONT color="green">613</FONT>                final SubHyperplane.SplitSubHyperplane&lt;S&gt; split = sub.split(hyperplane);<a name="line.613"></a>
<FONT color="green">614</FONT>                final SubHyperplane&lt;S&gt; plus  = recurseIntersection(node.getPlus(),  split.getPlus());<a name="line.614"></a>
<FONT color="green">615</FONT>                final SubHyperplane&lt;S&gt; minus = recurseIntersection(node.getMinus(), split.getMinus());<a name="line.615"></a>
<FONT color="green">616</FONT>                if (plus == null) {<a name="line.616"></a>
<FONT color="green">617</FONT>                    return minus;<a name="line.617"></a>
<FONT color="green">618</FONT>                } else if (minus == null) {<a name="line.618"></a>
<FONT color="green">619</FONT>                    return plus;<a name="line.619"></a>
<FONT color="green">620</FONT>                } else {<a name="line.620"></a>
<FONT color="green">621</FONT>                    return plus.reunite(minus);<a name="line.621"></a>
<FONT color="green">622</FONT>                }<a name="line.622"></a>
<FONT color="green">623</FONT>            default :<a name="line.623"></a>
<FONT color="green">624</FONT>                return recurseIntersection(node.getPlus(),<a name="line.624"></a>
<FONT color="green">625</FONT>                                           recurseIntersection(node.getMinus(), sub));<a name="line.625"></a>
<FONT color="green">626</FONT>            }<a name="line.626"></a>
<FONT color="green">627</FONT>    <a name="line.627"></a>
<FONT color="green">628</FONT>        }<a name="line.628"></a>
<FONT color="green">629</FONT>    <a name="line.629"></a>
<FONT color="green">630</FONT>        /** Transform a region.<a name="line.630"></a>
<FONT color="green">631</FONT>         * &lt;p&gt;Applying a transform to a region consist in applying the<a name="line.631"></a>
<FONT color="green">632</FONT>         * transform to all the hyperplanes of the underlying BSP tree and<a name="line.632"></a>
<FONT color="green">633</FONT>         * of the boundary (and also to the sub-hyperplanes embedded in<a name="line.633"></a>
<FONT color="green">634</FONT>         * these hyperplanes) and to the barycenter. The instance is not<a name="line.634"></a>
<FONT color="green">635</FONT>         * modified, a new instance is built.&lt;/p&gt;<a name="line.635"></a>
<FONT color="green">636</FONT>         * @param transform transform to apply<a name="line.636"></a>
<FONT color="green">637</FONT>         * @return a new region, resulting from the application of the<a name="line.637"></a>
<FONT color="green">638</FONT>         * transform to the instance<a name="line.638"></a>
<FONT color="green">639</FONT>         */<a name="line.639"></a>
<FONT color="green">640</FONT>        public AbstractRegion&lt;S, T&gt; applyTransform(final Transform&lt;S, T&gt; transform) {<a name="line.640"></a>
<FONT color="green">641</FONT>            return buildNew(recurseTransform(getTree(false), transform));<a name="line.641"></a>
<FONT color="green">642</FONT>        }<a name="line.642"></a>
<FONT color="green">643</FONT>    <a name="line.643"></a>
<FONT color="green">644</FONT>        /** Recursively transform an inside/outside BSP-tree.<a name="line.644"></a>
<FONT color="green">645</FONT>         * @param node current BSP tree node<a name="line.645"></a>
<FONT color="green">646</FONT>         * @param transform transform to apply<a name="line.646"></a>
<FONT color="green">647</FONT>         * @return a new tree<a name="line.647"></a>
<FONT color="green">648</FONT>         */<a name="line.648"></a>
<FONT color="green">649</FONT>        @SuppressWarnings("unchecked")<a name="line.649"></a>
<FONT color="green">650</FONT>        private BSPTree&lt;S&gt; recurseTransform(final BSPTree&lt;S&gt; node, final Transform&lt;S, T&gt; transform) {<a name="line.650"></a>
<FONT color="green">651</FONT>    <a name="line.651"></a>
<FONT color="green">652</FONT>            if (node.getCut() == null) {<a name="line.652"></a>
<FONT color="green">653</FONT>                return new BSPTree&lt;S&gt;(node.getAttribute());<a name="line.653"></a>
<FONT color="green">654</FONT>            }<a name="line.654"></a>
<FONT color="green">655</FONT>    <a name="line.655"></a>
<FONT color="green">656</FONT>            final SubHyperplane&lt;S&gt;  sub = node.getCut();<a name="line.656"></a>
<FONT color="green">657</FONT>            final SubHyperplane&lt;S&gt; tSub = ((AbstractSubHyperplane&lt;S, T&gt;) sub).applyTransform(transform);<a name="line.657"></a>
<FONT color="green">658</FONT>            BoundaryAttribute&lt;S&gt; attribute = (BoundaryAttribute&lt;S&gt;) node.getAttribute();<a name="line.658"></a>
<FONT color="green">659</FONT>            if (attribute != null) {<a name="line.659"></a>
<FONT color="green">660</FONT>                final SubHyperplane&lt;S&gt; tPO = (attribute.getPlusOutside() == null) ?<a name="line.660"></a>
<FONT color="green">661</FONT>                    null : ((AbstractSubHyperplane&lt;S, T&gt;) attribute.getPlusOutside()).applyTransform(transform);<a name="line.661"></a>
<FONT color="green">662</FONT>                final SubHyperplane&lt;S&gt; tPI = (attribute.getPlusInside()  == null) ?<a name="line.662"></a>
<FONT color="green">663</FONT>                    null  : ((AbstractSubHyperplane&lt;S, T&gt;) attribute.getPlusInside()).applyTransform(transform);<a name="line.663"></a>
<FONT color="green">664</FONT>                attribute = new BoundaryAttribute&lt;S&gt;(tPO, tPI);<a name="line.664"></a>
<FONT color="green">665</FONT>            }<a name="line.665"></a>
<FONT color="green">666</FONT>    <a name="line.666"></a>
<FONT color="green">667</FONT>            return new BSPTree&lt;S&gt;(tSub,<a name="line.667"></a>
<FONT color="green">668</FONT>                                        recurseTransform(node.getPlus(),  transform),<a name="line.668"></a>
<FONT color="green">669</FONT>                                        recurseTransform(node.getMinus(), transform),<a name="line.669"></a>
<FONT color="green">670</FONT>                                        attribute);<a name="line.670"></a>
<FONT color="green">671</FONT>    <a name="line.671"></a>
<FONT color="green">672</FONT>        }<a name="line.672"></a>
<FONT color="green">673</FONT>    <a name="line.673"></a>
<FONT color="green">674</FONT>    }<a name="line.674"></a>




























































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